Rethinking Retractions: Rethought

Four years ago I published what turned out to be one of my most popular blogposts: 'Rethinking Retractions'. In that post I related the story of how I managed to mess up the analysis in one of my papers, leading to a horrifying realisation when I gave my code to a colleague: a bug in my code had invalidated all our results. I had to retract the paper, before spending another year reanalysing the data correctly, and finally republishing our results in a new paper.

Since I wrote that blogpost I have found there are a lot of people out there who want to talk about retractions, the integrity of the scientific literature and the incentives researchers face around issues to do with scientific honesty.

Here a few of the things that have resulted from that original blogpost:

• David Duvenaud (who spotted the original bug in my code) created a presentation and a paper on the pitfalls of creating code for analysis, and sanity checks the analyst can use to avoid the same thing happening to them
• The story was picked up by Times Higher Education 
• I was invited to tell my story at a symposium at the World Conference on Research Integrity 2017. The symposium was organised by Elizabeth Moylan, who with co-authors wrote a proposal for a new system of post-publication article alterations. 
• After speaking at the symposium, the story of my retracted paper was covered by the founders of Retraction Watch in STAT and then by Science

Speaking at the World Conference on Research Integrity

Looking back now at the original blogpost, I can see the situation with some more distance and detachment. The most important thing I have to report, five years after the original cock-up and retraction, is that I never suffered any stigma from having to retract a paper. Sometimes scientists talk about retractions as if they are the end of the world. Of course, if you are forced to retract half of your life's work because you have been found to have been acting fraudulently then you may have to kiss your career goodbye. But the good news is that most scientists seem smart enough to tell the difference between an honest error and fraud! There are several proposals going around now to change the terminology around corrections and retractions of honest errors to avoid stigma, but I think the most important thing to say is that, by and large, the system works - if you have made an honest mistake you should go ahead and correct the literature, and trust your colleagues to see that you did the right thing.

Meanwhile, I'm just hoping I still have something to offer the scientific community beyond being 'the retraction guy'...

Analogues between student learning and machine learning

Back in 2014 I was trying to make some progress towards my docent (Swedish habilitation) by fulfilling the requirement to undertake formal pedagogic training. As it happens, I left Sweden before either could be completed, but I recently went back through my materials, and found this essay I had written as part of that course. In the absence of anything else to to do with it, here it now lies...

Introduction

Over time people have developed increasingly sophisticated theories of learning and education, and correspondingly teaching methods have changed and adapted. As a result, much is now known about what activities most promote student learning, and the differences between individuals in their learning techniques and strategies.

At the same time, computer scientists have developed increasingly powerful artificial intelligences. The creation of powerful computational methods for learning patterns, making predictions and understanding signals has drawn attention to a more mathematical understanding of how learning happens and can be facilitated.

Some of the parallels between these fields are obvious. For example, the development of artificial neural networks was driven by the analogy between these mathematical structures and the neuronal structure of the brain, and encouraged scientists to describe the brain from a computational perspective (e.g. in [Kovács, 1995]). However, the analogies between theories of learning in education and computer science are deeper than these surface resemblances, and go to the heart of what we consider useful information and knowledge, and what we mean by understanding.

In this report I will review elements of both the pedagogical and machine learning literature to draw attention to specific examples of what I consider to be direct analogues in these two fields, and how these analogies help organise our knowledge of the learning process and motivate approaches to student learning.

Learning to learn

When computer scientists first began creating an artificial intelligence, their first approach was to try to encode useful knowledge about the world directly in the machine, by explicitly inclusion in the computer’s programming. For example, in attempting to create a computer vision system that could recognise handwriting letters, the programmer would try to describe in computer code what an ‘A’ or a ‘B’ looked liked in terms that the computer could recognise in the images it received. However, this procedure generally proved dramatically ineffective. The sheer range of ways in which an ‘A’ can be written, the possible permutations on the basic design and the different angles and lighting that the computer could receive defeated the attempt to systematically describe the pattern in this top-down fashion.

Instead, success was first achieved in these tasks when researchers tried the radically different approach not of teaching the computer each concept individually, but instead teaching the computer how to learn itself. In 1959 Arthur Samuel defined machine learning as a ‘Field of study that gives computers the ability to learn without being explicitly programmed’ [Simon, 2013]. By providing the computer with algorithms that allowed it to observed examples of different letters, and learn to distinguish these itself from the examples, much greater success was possible in identifying the letters. In essence, by teaching the computer good methods for learning, the computer could gain much greater understanding itself, and with less input from the programmer.

The parallel here with the teacher-student relationship is very direct. A teacher is responsible, of course, for providing a great deal of information to a student. But the best teachers are more successful because they teach the students how to learn for the themselves, how to fit new examples into their existing understanding and how to seek the new information and examples they need. At the higher levels of tuition, encouraging and enabling this self-directed learning is essential. Anne Davis Toppins argues that within 30 minutes ‘I can convince most graduate students that they are self-directed learners’ [Toppins, 1987]. However, much as programmers initially tried to directly tell computers what they needed to know, before realising the greater efficiency of teaching them to learn for the themselves, so has the pedagogical approach taken a similar path [Gustafsson et al., 2011]:

'For some lecturers, thinking in terms of emphasising with and supporting the students’ learning and “teaching them to learn”, i.e. supporting them in their development of study skills, can constitute a new or different perspective. [...] Some teachers claim that since the students have studied for such a long time in other school situations, the higher education institution should not have to devote time to the learning procedure.'

In other words, there have been, and indeed still are many lecturers who view their role primarily in terms of transmitting information, rather than in developing the students’ abilities to think and learn for themselves.

Conceptual understanding

In the modern teaching literature, much importance is placed on aiming for, and testing students conceptual knowledge. That is, students are expected to learn not simply a series of factual statements, or isolated results, but instead to incorporate their knowledge into higher level abstract concepts that they can use to understand unfamiliar situations, solve unseen problems and extrapolate their knowledge to new domains. The prevailing doctrine of constructive alignment [Biggs, 1999] that forms the basis for recommended teaching approaches in European countries under the Bologna process is designed to make sure that teaching methods, student activities and assessment assignments all align towards this goal of promoting and testing whether students understand the ‘big picture’.

According to a computer scientists view of knowledge and information, there is a very good reason why we should aim to promote such a concept-centred approach for students. Identifying unifying principles that tie knowledge together and understanding how apparently different fields may link together reduces the amount and the complexity of the information that a student or computer must store, access and process, and maximises the effectiveness of extrapolating to new domains.

Consider as a simple example the data shown in figure 1. How can this data be effectively stored? The simplest method would be the record each pair of (x, y) co-ordinates. Assuming we use a 1 byte per number (single-precision floating point accuracy), this will take us 20 bytes (10 x’s, 10 y’s). But visually we can immediately recognise an important pattern; the data clearly lie along a straight line. If we know the gradient of this line we can immediate translate any value of x into a value of y. Therefore we can reproduce the whole data set by specifying just 12 numbers – the 10 values of x, one value for the intercept and one value of the gradient. Therefore by understanding one big idea, one concept about the data, that they lie along a line, we have almost halved the effort of learning and storing that information. Furthermore, we can now extrapolate to any new slue of x, immediately knowing the correct corresponding value of y. If we had simply memorised the 10 pairs of co-ordinates we would have no way to do this. In the field on machine-learning this line of reasoning has been formalised into the principles of Minimum Message Length or Minimum Description Length, first proposed by Chris Wallace [Wallace and Boulton, 1968] and Jorma Rissanen [Rissanen, 1978] respectively. This states that the best model, or description of data set is the one which requires the least information to store. Modern texts on machine-learning theory focus heavily on the superiority of the simplest possible models that enable reconstruction of the necessary information and stress the connection to the well established principle of Occam’s Razor (e.g. [MacKay, 2003]). Applications of machine learning theory to animal behaviour have further suggested that animals apply the same principles to maximise the value of their limited processing and storage capabilities [Mann et al., 2011], so it is likely that humans also apply similar methods

Figure 1: By observing conceptual patterns in the data we can reduce the amount of memory needed to store it, whether on a machine or in a human mind. In this simple example identifying the linear relation between the X and Y co-ordinates (Y = 2X), we need to store only the X values, the intercept and the gradient, reducing the number of stored numbers from 20 to 12.

An analogous example in student learning might be seen in teaching mathematics students to solve equations. The most naive way for students to learn how to solve a particular type of problem in an exam would be to observe many, many examples of the problem, remember the solution to each one and then attempt to identify a match in the exam and recall the solution for the matching equation. Such an approach, while not entirely unknown among students cramming for final exams, is likely doomed to failure. It requires an enormous amount of (trustworthy!) memory to store even a fraction of the possible problems one might see in the exam, and if a new problem is encountered there is no way to generalise from the known solutions to other equations in order to solve it. A much more efficient method is to learn general techniques that can be applied to any possible equation. In this case the student need only remember a few core principles and how to apply them. They can then solve both equations they have seen before, or new examples

Strategic learning

A common characteristic of high-achieving students is a strategic approach to learning. They have a good overview of what they need to learn to achieve their life goals. They set realistic but challenging learning goals for themselves to the end of learning this material. And they actively seek out information from teachers, reading materials and other sources to aid their learning. Whether their goals are intrinsic (interest in the subject, desire for knowledge) or extrinsic (obtaining a degree, getting a job), this strategic approach to learning systematically produces better outcomes than passively receiving whatever information is offered.

Analogously, in the field of machine learning, recent developments have tended more and more towards ideas termed ‘active learning’ [Settles, 2010]. The previous paradigm of simply offering many examples to the computer to learn from and then assessing or using the results of that process has been overturned. Instead, the programmer/mathematician devises a strategy for the computer to seek out new examples, based on what it wants to achieve (e.g. identifying written letters successfully) and what it currently knows. For example, if the computer has a good idea how to recognise an ‘A’, but frequently confuses a ‘U’ and a ‘V’, it will seek out or request more examples of these letters so that it can improve its knowledge. This way it does not waste time learning redundant material, but maximises the result of its effort by focusing on the most rewarding areas.

Likewise a high-performing student will focus their attentions on areas where they are weak and/or particularly crucial concepts that provide a pivot for understanding. They will ask their teachers for more feedback on their efforts in these areas, spend more time on mastering them and prioritise them ahead of areas of less importance or that are already understood. Mckeachie’s Teaching Tips [McKeachie and Svinicki, 2013] devotes a chapter to the importance encouraging strategic and self-regulated learning. One of their descriptions of a strategic learner states:

‘Strategic learners know when they understand new information and, perhaps more important, when they do not. When they encounter problems studying or learning, they use help-seeking strategies’.

This emphasis on the importance of know where understanding is lacking and the resultant help- seeking strategy perfectly aligns with what information theory tells us is the optimal way to gain useful knowledge.

Mckeachie’s Teaching Tips [McKeachie and Svinicki, 2013] also focuses on the importance of student learning goals. My own research in the field of active-learning corroborate this view, demonstrating that even when a learner has a good learning strategy, the success of that strategy depends intimately on the goals that the learner sets themselves. Indeed, without a suitable goal the learner is unable to define a useful strategy [Garnett et al., 2012]. Thus, in order to develop students strategic learning skills, it is essential first to help them define, and identify what their individual goals are. A student for whom this is an essential course, but who is otherwise uninterested, may be best helped by helping them to clarify what they wish to achieve (a certain final grade for instance), and then working with them to establish what strategy will most likely allow them to reach that outcome. A student with greater intrinsic motivation for the course may need help setting specific staged learning goals that enable a learning strategy. The teacher’s experience in understanding the most effective path through the material would therefore be essential in establishing effective goals that the student can then apply a strategy to achieve.

Discussion

While student and machine learning are clearly not direct parallels of each other (could one imagine a machine equivalent for tiredness, or skipping class to watch TV?), the analogies that do exist be- tween the two help us to understand why certain approaches to student learning are more successful than others, via the large body of technical knowledge that exists regarding how machines can be taught. In this report I have analysed a selection of those analogies, aiming to draw conclusions about how students should be taught.

In particular, a common theme of modern pedagogical approaches is to move from information transfer to a student directed learning approach. In a sense, computer scientists have been down this path already, switching from a programmer-led to a computer-led learning approach that has resulted in far superior learning outcomes. This should motivate and support the equivalent transition in student learning

In teaching computers how to think and learn, we have also needed to help them establish goals and strategies for learning, and this is now the forefront of machine learning research. The dramatic improvement in computer learning outcomes when well-developed strategies are employed should remind us that it is the manner in which the student approaches new information and requests help and feedback that matter at least as much as the amount of information they are presented with. Such knowledge demands that we devote time to monitoring and developing students learning strategies and discussing what they hope to achieve via our courses.

Students, like all of us, are presented with a great deal more information than they can easily process and digest. If computer science in the 21st century has taught us anything, it is the importance of identifying general patterns in the vast body of information we are now exposed to via the media, the Internet and other sources. Without relatively simple general principles, information can easily become overwhelming. That the same principle applies in student learning should not surprise us. How is a student to retain all the information we attempt to transfer to them without organising it into general principles rather than a huge array of specific cases? The content of any course therefore should revolve as much around this organisational structure as the raw information itself, demanding generalised understanding rather than specific regurgitation. Thankfully this is the direction modern pedagogy is taking, with such concepts of constructive alignment and the SOLO taxonomy.

References

[Biggs, 1999] Biggs, J. (1999). What the student does: teaching for enhanced learning. Higher Education Research & Development, 18(1):57–75.
[Garnett et al., 2012] Garnett, R., Krishnamurthy, Y., Xiong, X., Schneider, J., and Mann, R. (2012). Bayesian optimal active search and surveying. In Proceedings of the International Con- ference of Machine Learning.
[Gustafsson et al., 2011] Gustafsson, C., Fransson, G., Morberg, ̊A., and Nordqvist, I. (2011). Teaching and learning in higher education: challenges and possibilities.
[Kovács, 1995] Kovács, I. (1995). Maturational windows and adult cortical plasticity, volume 24. Westview Press.
[MacKay, 2003] MacKay, D. J. C. (2003). Information Theory, Inference and Learning Algorithms. Cambridge: Cambridge University Press.
[Mann et al., 2011] Mann, R., Freeman, R., Osborne, M., Garnett, R., Armstrong, C., Meade, J., Biro, D., Guilford, T., and Roberts, S. (2011). Objectively identifying landmark use and predicting flight trajectories of the homing pigeon using gaussian processes. Journal of The Royal Society Interface, 8(55):210–219.
[McKeachie and Svinicki, 2013] McKeachie, W. and Svinicki, M. (2013). McKeachie’s teaching tips. Cengage Learning.
[Rissanen, 1978] Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14(5):465–471.
[Settles, 2010] Settles, B. (2010). Active learning literature survey. University of Wisconsin, Madison, 52:55–66.
[Simon, 2013] Simon, P. (2013). Too Big to Ignore: The Business Case for Big Data. John Wiley & Sons.
[Toppins, 1987] Toppins, A. D. (1987). Teaching students to teach themselves. College Teaching, 35(3):95–99.
[Wallace and Boulton, 1968] Wallace, C. S. and Boulton, D. M. (1968). An information measure for classification. The Computer Journal, 11(2):185–194.

General election 2017: Opinion Polls vs Betting Markets

Update, June 9: The results are in, and the BBC gives the vote share for each party. Although the polls gave a wide variety of different predictions between different polling companies, the average of the polls appears to have outperformed the betting markets again!



See my recent article in The Conversation for some reasons why betting markets may have been performing so badly in predicting elections and referenda in recent years, or read the original research here

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Tomorrow is the polling day in the UK General Election 2017 (make sure you vote!). Today's news will be full of the latest opinion poll numbers, and pundits making predictions. Increasingly people are also looking to betting and prediction markets to get an idea of what is likely to happen as well. Both opinion polls and betting markets have made some very significant errors in recent years. Before the Brexit referendum I did an analysis of what bets on Betfair were telling us about the predicted vote share for Leave/Remain. Punters got that one wrong, just like the election of Trump in the USA, while polls were more accurate in predicting tight races.

Before we go to the polls tomorrow, lets compare what opinion polls and betting markets are telling us, so we can evaluate which is more accurate on this occasion. I'll focus simply on raw vote share for the two main parties (ignoring constituency effects), and I'll use the Financial Times poll-of-polls as a benchmark for the opinion polls and Betfair's vote share markets for betting markets.

First the opinion polls: https://ig.ft.com/elections/uk/2017/polls/



This gives a central forecast of Conservatives on 43%, Labour on 37%

To calculate the predicted vote share from Betfair I'll be repeating the analysis I did here (see previous post for R code), fitting a beta-distribution to the vote share divisions given on the market. I've taken screenshots of the Conservative and Labour markets, as these will no doubt change after I post this:

Conservative:



Labour:



Performing the analysis to get the predicted vote share gives the following results:


This puts the Conservatives on 44% and Labour on 34% - almost identical for the Conservatives as the opinion poll, but somewhat lower for Labour.

Labour have recently surged in the polls from a very low position. It seems that the betting markets don't fully trust this. Come tomorrow night we'll have a good idea which of the polls or the market has been more accurate.